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      "cell_type": "code",
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      "source": [
        "%matplotlib inline"
      ]
    },
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      "metadata": {},
      "source": [
        "\n# Robust linear model estimation using RANSAC\n\n\nIn this example we see how to robustly fit a linear model to faulty data using\nthe RANSAC algorithm.\n\n\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
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      "source": [
        "import numpy as np\nfrom matplotlib import pyplot as plt\n\nfrom sklearn import linear_model, datasets\n\n\nn_samples = 1000\nn_outliers = 50\n\n\nX, y, coef = datasets.make_regression(n_samples=n_samples, n_features=1,\n                                      n_informative=1, noise=10,\n                                      coef=True, random_state=0)\n\n# Add outlier data\nnp.random.seed(0)\nX[:n_outliers] = 3 + 0.5 * np.random.normal(size=(n_outliers, 1))\ny[:n_outliers] = -3 + 10 * np.random.normal(size=n_outliers)\n\n# Fit line using all data\nlr = linear_model.LinearRegression()\nlr.fit(X, y)\n\n# Robustly fit linear model with RANSAC algorithm\nransac = linear_model.RANSACRegressor()\nransac.fit(X, y)\ninlier_mask = ransac.inlier_mask_\noutlier_mask = np.logical_not(inlier_mask)\n\n# Predict data of estimated models\nline_X = np.arange(X.min(), X.max())[:, np.newaxis]\nline_y = lr.predict(line_X)\nline_y_ransac = ransac.predict(line_X)\n\n# Compare estimated coefficients\nprint(\"Estimated coefficients (true, linear regression, RANSAC):\")\nprint(coef, lr.coef_, ransac.estimator_.coef_)\n\nlw = 2\nplt.scatter(X[inlier_mask], y[inlier_mask], color='yellowgreen', marker='.',\n            label='Inliers')\nplt.scatter(X[outlier_mask], y[outlier_mask], color='gold', marker='.',\n            label='Outliers')\nplt.plot(line_X, line_y, color='navy', linewidth=lw, label='Linear regressor')\nplt.plot(line_X, line_y_ransac, color='cornflowerblue', linewidth=lw,\n         label='RANSAC regressor')\nplt.legend(loc='lower right')\nplt.xlabel(\"Input\")\nplt.ylabel(\"Response\")\nplt.show()"
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